It appears he had wealthy parents so that's a good start. So here's my shot at it:
Nicky joins the army rather than the clergy. His family uses their wealth to give him an officer position. He shows a lot of military promise and in Constantine's campaign against Maxentius he catches Constantine's attention. Constantine promotes him to his inner circle, and eventually he's trusted with a governership of the Diocese of Asia, and eventually leads some forces of his own.
Fast forward to Constantine's death. ITTL, Constans has died prior to Constantine's ascension. Constantine II loses a civil war to Constantius, who soon after dies from disease on his way back to Constantinople. Nicky, who had earned the trust of Constantius and was the commander of his personal guard, is promoted emperor by the troops. Assassins are sent out to Cappadocia to kill Julian and extinguish Constantine's line. It's 339.
Nicky appoints his 30 year old son as Caesar, rules for the next 4 years, and then dies, leaving his son emperor.